117328 Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be two functions defined by \(f(x)=\log _e\left(x^2+1\right)-e^{-x}+1\) and \(g(x)\) \(=\frac{1-2 e^{2 x}}{e^x}\). Then, for which of the following range of \(\alpha\), the inequality
\(\mathbf{f}\left(\mathbf{g}\left(\frac{(\alpha-1)^2}{3}\right)\right)>\mathbf{f}\left(\mathbf{g}\left(\alpha-\frac{5}{3}\right)\right)\) holds?

117329 The domain of the function
\(f(x)=\frac{\cos ^{-1}\left(\frac{x^2-5 x+6}{x^2-9}\right)}{\log _e\left(x^2-3 x+2\right)}\) is

117330 What is the range the function \(h(x)=\frac{x-2}{x+3}\) ?

117331 If \(f: R \rightarrow[-1,1]\) and \(g: R \rightarrow A\) are two subjective mappings and \(\sin \left(g(x)-\frac{\pi}{3}\right)=\frac{f(x)}{2} \sqrt{4-f^2(x)}\), then \(A=\)

117332 The domain of the function \(f(x)=\sqrt{\frac{4-x^2}{[x]+2}}\), where \([x]\) denotes the greatest integer not more than \(x\), is

117328 Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be two functions defined by \(f(x)=\log _e\left(x^2+1\right)-e^{-x}+1\) and \(g(x)\) \(=\frac{1-2 e^{2 x}}{e^x}\). Then, for which of the following range of \(\alpha\), the inequality
\(\mathbf{f}\left(\mathbf{g}\left(\frac{(\alpha-1)^2}{3}\right)\right)>\mathbf{f}\left(\mathbf{g}\left(\alpha-\frac{5}{3}\right)\right)\) holds?

117329 The domain of the function
\(f(x)=\frac{\cos ^{-1}\left(\frac{x^2-5 x+6}{x^2-9}\right)}{\log _e\left(x^2-3 x+2\right)}\) is

117330 What is the range the function \(h(x)=\frac{x-2}{x+3}\) ?

117331 If \(f: R \rightarrow[-1,1]\) and \(g: R \rightarrow A\) are two subjective mappings and \(\sin \left(g(x)-\frac{\pi}{3}\right)=\frac{f(x)}{2} \sqrt{4-f^2(x)}\), then \(A=\)

117332 The domain of the function \(f(x)=\sqrt{\frac{4-x^2}{[x]+2}}\), where \([x]\) denotes the greatest integer not more than \(x\), is

117328 Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be two functions defined by \(f(x)=\log _e\left(x^2+1\right)-e^{-x}+1\) and \(g(x)\) \(=\frac{1-2 e^{2 x}}{e^x}\). Then, for which of the following range of \(\alpha\), the inequality
\(\mathbf{f}\left(\mathbf{g}\left(\frac{(\alpha-1)^2}{3}\right)\right)>\mathbf{f}\left(\mathbf{g}\left(\alpha-\frac{5}{3}\right)\right)\) holds?

117329 The domain of the function
\(f(x)=\frac{\cos ^{-1}\left(\frac{x^2-5 x+6}{x^2-9}\right)}{\log _e\left(x^2-3 x+2\right)}\) is

117330 What is the range the function \(h(x)=\frac{x-2}{x+3}\) ?

117331 If \(f: R \rightarrow[-1,1]\) and \(g: R \rightarrow A\) are two subjective mappings and \(\sin \left(g(x)-\frac{\pi}{3}\right)=\frac{f(x)}{2} \sqrt{4-f^2(x)}\), then \(A=\)

117332 The domain of the function \(f(x)=\sqrt{\frac{4-x^2}{[x]+2}}\), where \([x]\) denotes the greatest integer not more than \(x\), is

117328 Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be two functions defined by \(f(x)=\log _e\left(x^2+1\right)-e^{-x}+1\) and \(g(x)\) \(=\frac{1-2 e^{2 x}}{e^x}\). Then, for which of the following range of \(\alpha\), the inequality
\(\mathbf{f}\left(\mathbf{g}\left(\frac{(\alpha-1)^2}{3}\right)\right)>\mathbf{f}\left(\mathbf{g}\left(\alpha-\frac{5}{3}\right)\right)\) holds?

117329 The domain of the function
\(f(x)=\frac{\cos ^{-1}\left(\frac{x^2-5 x+6}{x^2-9}\right)}{\log _e\left(x^2-3 x+2\right)}\) is

117330 What is the range the function \(h(x)=\frac{x-2}{x+3}\) ?

117331 If \(f: R \rightarrow[-1,1]\) and \(g: R \rightarrow A\) are two subjective mappings and \(\sin \left(g(x)-\frac{\pi}{3}\right)=\frac{f(x)}{2} \sqrt{4-f^2(x)}\), then \(A=\)

117332 The domain of the function \(f(x)=\sqrt{\frac{4-x^2}{[x]+2}}\), where \([x]\) denotes the greatest integer not more than \(x\), is

117328 Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be two functions defined by \(f(x)=\log _e\left(x^2+1\right)-e^{-x}+1\) and \(g(x)\) \(=\frac{1-2 e^{2 x}}{e^x}\). Then, for which of the following range of \(\alpha\), the inequality
\(\mathbf{f}\left(\mathbf{g}\left(\frac{(\alpha-1)^2}{3}\right)\right)>\mathbf{f}\left(\mathbf{g}\left(\alpha-\frac{5}{3}\right)\right)\) holds?

117329 The domain of the function
\(f(x)=\frac{\cos ^{-1}\left(\frac{x^2-5 x+6}{x^2-9}\right)}{\log _e\left(x^2-3 x+2\right)}\) is

117330 What is the range the function \(h(x)=\frac{x-2}{x+3}\) ?

117331 If \(f: R \rightarrow[-1,1]\) and \(g: R \rightarrow A\) are two subjective mappings and \(\sin \left(g(x)-\frac{\pi}{3}\right)=\frac{f(x)}{2} \sqrt{4-f^2(x)}\), then \(A=\)

117332 The domain of the function \(f(x)=\sqrt{\frac{4-x^2}{[x]+2}}\), where \([x]\) denotes the greatest integer not more than \(x\), is